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Look to Newegg.com. You could probably upgrade the internal one if you're so inclined. Just be really careful.
 
Installing an internal DVD burner into the eMac isn't very difficult (at least compared to the hard drive). Just make sure whatever new drive you get is natively recognized by OS X and supports disc burning.
 
Me, I'd just go to Newegg and spend the $40 on a Pioneer 111D, put it in the eMac directly, and be done with it. Fast, cheap, supported natively, and a nice burner. If you don't want to crack open the eMac, you can get an external firewire case for it for about $30 or so.
 
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